A prime challenge to our understanding of galaxy formation concerns the 
scarcity of dwarf galaxies compared with the numerous low-mass halos expected 
in the current ΛCDM paradigm. This is usually accounted for by assuming that 
energetic feedback from evolving stars confines dwarf galaxy formation to 
relatively massive halos spanning a narrow mass range. I will highlight a 
number of observations that may be used to test this assumption and discuss the 
puzzles and challenges that arise from this analysis. I will also discuss a 
number of challenges that ΛCDM faces on the scale of dwarf galaxies and their 
possible resolutions.